COMPARISON OF OBJECTIVES OF THE SAME POWER 47 



also, and attains its maximum, not in the case of the air-angle of 

 180 (when it is exactly equivalent to the oil-angle of 82), but is 

 greatest at the oil-angle of 180. 



If we assume the objectives to have the same power throughout, 

 we get rid of one of the factors of the ratio, and we have only to 

 compare the diameters of the emergent beams, and can represent 

 their relations by diagrams. Fig. 31 illustrates five cases of different 

 apertures of J-in. objectives 

 viz. those of dry objectives of 

 60, 97, and 180 air-angle, a' 

 water-immersion of 180 water- 

 angle, and an oil -immersion of 

 1 80 oil-angle . The inner dotted 

 circles in the two latter cases 

 are of the same size as that 

 corresponding to the 180 air- 

 angle. 



A dry objective of the full 

 maximum air-angle of 180 is 

 only able (whether the first sur- 

 face is plane or concave) to utilise 

 a diameter of back lens equal to 

 twice the focal length, while an 

 immersion lens of even only 100 

 (in glass) requires and utilises a 

 larger diameter, i.e. it is able 

 to transmit more rays from the 

 object to the image than any 

 dry objective is capable of trans- 

 mitting. Whenever the angle of 

 an immersion lens exceeds twice 

 the critical angle for the immer- 

 sion-fluid, i.e. 96 for water or 

 82 for oil, its aperture is in ex- 

 cess of that of a dry objective of 

 180. 



Having settled the principle, 

 it was still necessary, however, 

 to find a proper notation for com- 

 paring apertures. The astrono- 

 mer can compare the apertures of his various telescopes by simply 

 expressing them in inches ; but this is obviously not available to 

 the microscopist, who has to deal with the ratio of two varying 

 quantities. 



Professor Abbe here again conferred a boon upon microscopists by 

 his discovery (in 1873, independently confirmed by Professor Helm- 

 holtz shortly afterwards) that a general relation existed between the 

 pencil admitted into the front of the objective and that emerging 

 from the back of the objective, so that the ratio of the semi -diameter 

 of the emergent pencil to the focal length of the objective could be 







Numerical Aperture 



1-52 

 = 180 oil-angle. 



Numerical Aperture 



1-33 

 = 180 water-angle. 



Numerical Aperture 



1-00 



= 180 air-angle 

 = 96 water-angle 

 = 82 oil-angle. 



Numerical Aperture 



75 

 = 97 air-angle. 



Numerical Aperture 



50 

 = 60 air-angle. 



FIG. 31. Eelative diameters of the (uti- 

 lised) back lenses of various dry and 

 immersion objectives of the same 

 power (|) from an air-angle of 60 to 

 an oil-angle of 180. 



